Degenerate conformal block and the spectral curve.
Let us suppose that one of the fields in the conformal block is degenerate at a level \(L\) , which means it is simultaneously a primary field and a level \(L\)  descendant. Then, the corresponding conformal block satisfies an equation of order \(L\)  [1]}, [2]}, [3]}, [4]}, [5]}. For instance,
\((b^2L_{-1}^2-L_{-2})V_{1/2b}(z)\)  is a primary field, i.e., \(V_{1/2b}(z)\)  is degenerate at the second level. Then, the equation for the 5-point block with the degenerate field at \(z\) :
\(\bigg [ b^2z(z-1)\partial _z^2+(2z-1)\partial _z-\underbrace{{q(q\!-\!1)\over z\!-\!q}\partial _q\!+\text{rational function of }q}_{\text{check-operator}}\!\bigg ]G_5(z|0,q,1,\infty )=0,\!\!\!\!\) 
